I would highly recommend, spend the extra money and get fluorescent (CFL) light bulbs instead, otherwise you'll spend it on deep cycle batteries and extra duty inverters and it's not going to be cheap, even then I doubt they'll last long, you're talking about consuming an entire kilowatt hour at ten times the rate (i.e.: 120v / 12)...

To my understanding that inverter is going to have to get the batteries to feed 5,000 watts at 12v in order to roughly compensate for the difference in voltage and my math may not be exactly the way it is but I know it works somewhere along those lines.

With CFL bulbs you can likely reduce the consumption down to around 175 watts total (at 120v), that would be a whole lot easier on both the inverter and the batteries (yes, probably still need more than one), might be a bit of a trick to find them types of bulbs in CFL but in recent years they have come a long ways, they even make outdoor spot and flood lamps in the CFL version now...

You might even be able to find a load of 12v LED lights, thou this is going to be tricky and rather expensive as well.

The only inverters I've ever used are the cigarette lighter types. Im sure those won't work at all. Maybe there is some kind of super inverter out there capable of pushing 1000watts, but I'm unaware of it. If there is, it's probably more expensive than a 1000watt generator. If I remember correctly;
WATTS=VoltsXAmps

If you need 1000 watts off of 12 Volts, you'd be running like 83 AMPS. Not gonna happen.

I don't know the in's and out's of big light's through inverter's and battery's, but if this is a spotlighting some kind of fish deal, i've seen a lot of little boat's with big, bright light's. Someone has figured it out, a marine mechanic might be the guy to ask.

sounds like a good plan and good luck! FYI- when you get the chance, check into a honda or yamaha genny. They are so quiet it will blow your mind. I just bought a Yamaha 2400 watt for my camper at deer camp- can't even hear it outside when the tv or furnace is on.

Use 12 volt lights; no need for a inverter or generator. Perhaps headlights or spotlights would suit your situation. Above advice is good...if you can find fluorescent or Led the power consumption is a lot less; batt would last a lot longer. Led headlights are not so unusual anymore.